Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
Answer:
C. 11
Step-by-step explanation:
Substituting, we have ...
8{80, 19, 11} ?= 88
{640, 152, 88} ?= 88
The value from the set that makes the equation true is x = 11.
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<em>Alternate methods of solution (other than substitution)</em>
It can be easier to make use of your knowledge of factoring:
8x = 8·11
x = 11
Or to make use of your knowledge of numbers (place value):
8·10 = 80
so x will not be very different from 10.
Answer:
11 17/21
Step-by-step explanation:
They're the same because squares have 90 degree angles and that cut in half with a diagonal would make the angle acute at a 45 degree angle so depending on the lengths of the sides depends on the area, the angles have nothing to do with it because all squared have 4 right angles
E porque ya lo use y es facil
